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Simultaneous estimation of quantile curves using quantile sheets

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  • Sabine Schnabel
  • Paul Eilers

Abstract

The results of quantile smoothing often show crossing curves, in particular, for small data sets. We define a surface, called a quantile sheet, on the domain of the independent variable and the probability. Any desired quantile curve is obtained by evaluating the sheet for a fixed probability. This sheet is modeled by $$P$$ -splines in form of tensor products of $$B$$ -splines with difference penalties on the array of coefficients. The amount of smoothing is optimized by cross-validation. An application for reference growth curves for children is presented. Copyright The Author(s) 2013

Suggested Citation

  • Sabine Schnabel & Paul Eilers, 2013. "Simultaneous estimation of quantile curves using quantile sheets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 77-87, January.
    • Handle: RePEc:spr:alstar:v:97:y:2013:i:1:p:77-87
    DOI: 10.1007/s10182-012-0198-1
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    References listed on IDEAS

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    11. Burdejova, P. & Härdle, W. & Kokoszka, P. & Xiong, Q., 2017. "Change point and trend analyses of annual expectile curves of tropical storms," Econometrics and Statistics, Elsevier, vol. 1(C), pages 101-117.

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